Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks

Robert M. Ziff

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arXiv · 0903.4678

Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks

Robert M. Ziff

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Abstract

The growth of two-dimensional lattice bond percolation clusters through a cooperative Achlioptas-type of process, where the choice of which bond to occupy next depends upon the masses of the clusters it connects, is shown to go through an explosive, first-order kinetic phase transition with a sharp jump in the mass of the largest cluster as the number of bonds is increased. The critical behavior of this growth model is shown to be of a different universality class than standard percolation.

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Robert M. Ziff. 2009-07-03. Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks. https://arxiv.org/abs/0903.4678

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